A review of optimal transport in image processing

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  • 1. School of Mathematics and Physics, Hebei University of Engineering, Handan 056038, Hebei, China;
    2. School of Mathematics, HarbinInstitute of Technology, Harbin 150001, China

Received date: 2019-03-31

  Online published: 2019-09-09

Abstract

The optimal transport problem which has attracted wide attentions in many fields in recent years, is a special kind of optimization problem discussed in the probabilistic measure space. In order to overcome the disadvantages of traditional optimal transport models, such as complex computation and lack of regularity, many different kinds of improved optimal transport models and algorithms are proposed to deal with various practical problems. Firstly, this paper briefly describes the basic theory and methods of optimal transport, and further introduces the concept of Wasserstein distance and Wasserstein barycenters. And then, the discrete optimal transport model and the improved regularization models are discussed. Besides, a short summary of the algorithms to solve optimal transport problem is given. Then, from Wasserstein distance aspect, a review of applications in several areas of image processing is briefly discussed. At last, the further research work is prospected.

Cite this article

MA Litao, BIAN Wei . A review of optimal transport in image processing[J]. Operations Research Transactions, 2019 , 23(3) : 109 -125 . DOI: 10.15960/j.cnki.issn.1007-6093.2019.03.008

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